What is the derivative of ln(arcsin(x^2)) ?

The derivative of ln(arcsin(x^2)) is (2x)/(arcsin(x^2)sqrt(1-x^4))

What is the first derivative of ln(arcsin(x^2)) ?

The first derivative of ln(arcsin(x^2)) is (2x)/(arcsin(x^2)sqrt(1-x^4))

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\frac{d}{d x} (ln (arcsin (x^{2})))

\frac{2 x}{arcsin ( x ^{2} ) 1 - x ^{4}}

Solution steps

\frac{d}{d x} (ln (arcsin (x^{2})))

Apply the chain rule:

\frac{1}{arcsin ( x ^{2} )} \frac{d}{d x} (arcsin (x^{2}))

= \frac{1}{arcsin ( x ^{2} )} \frac{d}{d x} (arcsin (x^{2}))

\frac{d}{d x} (arcsin (x^{2})) = \frac{2 x}{1 - x ^{4}}

= \frac{1}{arcsin ( x ^{2} )} \cdot \frac{2 x}{1 - x ^{4}}

Simplify

\frac{1}{arcsin ( x ^{2} )} \cdot \frac{2 x}{1 - x ^{4}} : \frac{2 x}{arcsin ( x ^{2} ) 1 - x ^{4}}

= \frac{2 x}{arcsin ( x ^{2} ) 1 - x ^{4}}

\int (x^{3} - 6 x) d x

\frac{d}{d x} (x^{3} - 6 x^{2} - 15 x + 40)

x \to 0 lim (- \frac{7}{1 - 7 x})

y = x^{2} + 2, (1, 4)

y = 9 cos (x), (\frac{π}{3}, 4.5)

What is the derivative of ln(arcsin(x^2)) ?
The derivative of ln(arcsin(x^2)) is (2x)/(arcsin(x^2)sqrt(1-x^4))
What is the first derivative of ln(arcsin(x^2)) ?
The first derivative of ln(arcsin(x^2)) is (2x)/(arcsin(x^2)sqrt(1-x^4))